(a) Resistors given as `R_(1), R_(2) and R_(3)` are connected in series to a battery V. Draw the circuit diagram showing the arrangement. Derive an expression for the equivalent resistance of the combination.
(b) If `R_(1)=10 Omega, R_(2)=20 Omega and R_(3)=30 Omega`, calculate the effective resistance when they are connected in series to a battery of 6 V. Also find the current flowing in the circuit.

Explanation

### Solution:

**(a)** To draw the circuit diagram for resistors \( R_1, R_2, \) and \( R_3 \) connected in series to a battery \( V \):

1. **Draw the Battery**: Start by drawing a battery symbol, which consists of two parallel lines (one longer and one shorter).
2. **Connect Resistors in Series**: Draw three resistors in a straight line connected one after the other. Label them as \( R_1, R_2, \) and \( R_3 \).
3. **Indicate Current Flow**: Draw arrows to indicate the direction of current flow from the positive terminal of the battery through the resistors and back to the negative terminal.

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